I would like to know whether the samples that are grouped together in the above scenario have any common genetic variants among them. In other words, are there 'secondary' variants elsewhere in the exome (other than the X gene) that are common amongst patients that suffer from the same symptoms.

- I want to find common variants for the bleeding symptom, does the common variants differ between the case1 and case2 or not?

case1: I am comparing individual VCF file (sample2.vcf, sample5.vcf and sample6.vcf) and filtering the common variants

case2: I am extracting just the sample2, sample5, and sample6 from the single VCF file with all 25 samples in it

As the above example, I would like to find common variants at the family level as well.

The differences will be in INFO column (especially with AC, AN etc. tags). The combined VCF will have aggregated statistics for those tags. Other than that, I don't think there would be any differences.